-2x +1, if x s -1 For the function f(x)= 2,1. ifxs- 6. I. Evaluate: a) f(-2) b) f(-1) c) f(o) II. Graph the function f(x) 5 2 -3 -5 7. Expand the following logarithmic expression using the prope...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
1) Allow f(x) = x3, and g(x) = 2x. Determine f(g(1)). 2) Enter the formula for a sine function with an amplitude of 5, a period of 90 degrees, a shift of 45 degrees to the right and 3 units upwards. Determine the exact value of the expression sin (v) + cos (v) given that tan (v) = 7/3. 3) Solve the equations in the range 180≤x≤360 degrees. Answer with one decimal. a) tan (x) = 3.2 (I would like...
(b) In diffraction theory, it is sometimes necessary to evaluate the function sine f (x) = for small to moderate (positive) values of the variable x. One way to do this is to make use of the Taylor-MacLaurin series θ2n-1 θ-31+5!-...+ (-1)"-1 sin θ = (2n-1+ Rr) with remainder term θ2n I lere, ξ is some number in the interval 0 < ξ < θ. Derive a Taylor-series expression for f(x), and give an upper bound for the crror when...
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Given h(x) = 2x + 9 and f(x) = 1/6x +5 Evaluate the composite function h[f(6)]
Question 3 (5 points) Evaluate the logarithmic expression. Graph f(x) = logļx-3 ༠ ༠ ༠ ༠ ༠ ༠ ༡ པ ས ས ས ས ས ས ས ས ས : । पाते Question 4 (5 points) In 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump for women was 70.0 inches, while the winning jump for men was 86.5 inches. Since then, the winning jump for women has increased by...
Evaluate the indicated function, where f(x)= x^2-4x +3 and g(x) = 2x-6 (f/g)(1/2)
Graph the function. f(x) 1-3 ifx<-1 2x+1 tfx 2-1 o 3 2+ O 1 --- +1 cf +4 KA + 1
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...